Henri & Renaud Lifchitz's PRP Top records

What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!

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1-250	251-500	501-750	751-1000	1001-1250	1251-1500	1501-1750	1751-2000
2001-2250	2251-2500	2501-2750	2751-3000	3001-3250	3251-3500	3501-3750	3751-4000
4001-4250	4251-4500	4501-4750	4751-5000	5001-5250	5251-5500	5501-5750	5751-6000
6001-6250	6251-6500	6501-6750	6751-7000	7001-7250	7251-7500	7501-7750	7751-8000
8001-8250	8251-8500	8501-8750	8751-9000	9001-9250	9251-9500	9501-9750	9751-10000

Rank	Probable prime	Digits (> 30000)	Who ?	When ?
9001	12^47861-35	51651	Lelio R Paula	12/2012
9002	6^66369-26813	51646	Enzo Doria	03/2013
9003	Phi(83967,10)/2272482889	51639	Maksym Voznyy	01/2010
9004	2^171524+153	51634	Lelio R Paula	02/2011
9005	(2^171516-509203)/4869	51628	Lelio R Paula	05/2012
9006	(12589^12589+323)/2^5/3	51613	Makoto Morimoto	07/2016
9007	5*10^51608-81	51609	Robert Price	04/2017
9008	(lucasV(1,2,342870)+2)/(1325933242617)	51597	Mike Oakes	03/2017
9009	10171^12872-12872^10171	51583	Norbert Schneider	04/2017
9010	2^171351-112677	51582	Enzo Doria	06/2014
9011	(12583^12583+1695)/2/11^2/7535089	51579	Makoto Morimoto	07/2016
9012	9818^12919-12919^9818	51573	Norbert Schneider	05/2017
9013	(3^108091+7)/382	51570	Lelio R Paula	03/2012
9015	2^171287-3187	51563	Yves Minet	04/2009
9014	-lucasV(-1,2,342569)	51563	Mike Oakes	02/2017
9016	2^171280-1030709	51561	Paul Bourdelais	11/2012
9017	13300^7527+7527^13300	51560	Hans Havermann	05/2016
9018	2^171268+73711	51557	Enzo Doria	04/2016
9019	(17*2^171266+1)/6963	51554	Lelio R Paula	01/2012
9020	(1964814^8192+1)/65537	51551	Lelio R Paula	06/2013
9021	4*10^51530-63	51531	Robert Price	12/2016
9022	3*6^66216-5	51527	Lelio R Paula	09/2014
9023	12569^12569+540	51525	Makoto Morimoto	07/2016
9024	2^171152-2459	51522	Yves Minet	07/2014
9025	(13*10^51511-1)/3	51512	Robert Price	12/2014
9026	5*10^51508+3	51509	Dmitry Domanov	11/2010
9027	3^107919-46	51491	Lelio R Paula	07/2012
9028	4*10^51489+87	51490	Robert Price	05/2016
9029	(22699*2^171030+1)/3029	51487	Lelio R Paula	05/2014
9030	2^171028-3239	51485	Yves Minet	12/2014
9031	2^170992-954209	51474	Paul Bourdelais	11/2012
9032	76^27367+75	51473	Norbert Schneider	11/2012
9033	6007^13620-102	51466	Enzo Doria	07/2012
9034	gcd(V(923445),5F(184689)(F(184689)-1)+1)	51462	Serge Batalov	04/2015
9035	t(194442)	51459	Robert Price	08/2014
9036	(22*10^51457+161)/3	51458	Robert Price	02/2017
9037	9^53921+8^(53921+1)	51454	Robert Price	06/2016
9039	2^170921-16995	51453	Lelio R Paula	08/2011
9038	2^170922-2135	51453	Yves Minet	06/2013
9040	4357^14138-120	51451	Enzo Doria	06/2012
9041	153^23550+2	51450	Lelio R Paula	05/2013
9042	(3^107833+2)/25	51449	Lelio R Paula	03/2012
9043	7*10^51440-47	51441	Robert Price	02/2017
9044	(10^51431-3^51431)/7	51431	Robert Price	06/2011
9045	U(250849)	51425	Michael Porter	08/2007
9046	(86*10^51424-41)/9	51425	Robert Price	11/2015
9048	12^47649+7	51422	Lelio R Paula	12/2012
9047	(25*10^51421+11)/9	51422	Robert Price	03/2015
9049	3^107768+2660	51419	Lelio R Paula	07/2012
9050	2^170784-6555	51412	Lelio R Paula	05/2009
9051	(-lucasV(1,2,341584)-2)/79	51412	Mike Oakes	03/2017
9052	51^30106+2	51409	Lelio R Paula	05/2013
9053	5^73546-12806	51407	Enzo Doria	02/2013
9054	(12545^12545+12546^12546)/(1584571*19137767639)	51404	Walter Nissen	09/2014
9055	(3^107735-4)/431	51401	Lelio R Paula	03/2012
9056	20^39505-6483	51398	Enzo Doria	03/2013
9057	2^170736-15197	51397	Enzo Doria	04/2013
9058	2^170737-3823	51397	Yves Minet	04/2017
9059	(12541^12541+393)/2/563	51395	Makoto Morimoto	07/2016
9060	9^53857-8^53857	51393	Jean-Louis Charton	11/2004
9061	5^73524-14426	51392	Enzo Doria	02/2013
9062	2^170712+243	51390	Lelio R Paula	10/2011
9063	(15*2^170713+1)/1793	51388	Lelio R Paula	07/2012
9064	(2^170702+9)/1261	51384	Lelio R Paula	01/2012
9065	283^20956+20956^283	51380	Norbert Schneider	08/2014
9066	2^170665-31	51376	Lelio R Paula	01/2011
9067	11^49330-12	51372	Lelio R Paula	01/2013
9068	(25*10^51366-73)/3	51367	Robert Price	09/2016
9069	5^73486-2^73487	51365	Mike Oakes	10/2010
9070	(10^51364+119)/3	51364	Serge Batalov	12/2014
9071	15^43672+68	51363	Lelio R Paula	01/2013
9072	2^170609-113143	51359	Enzo Doria	07/2014
9073	760^17827-759^17827	51357	Jean-Louis Charton	12/2010
9074	(22699*2^170592+1)/4435	51355	Lelio R Paula	05/2014
9075	8*7^60767+3	51355	Lelio R Paula	09/2014
9076	5^73452-20646	51341	Enzo Doria	03/2013
9077	2^170531-230407	51335	Gary Barnes	08/2009
9078	35^33243-2112	51330	Enzo Doria	03/2013
9079	(1845768^8192+1)/65537	51328	Lelio R Paula	06/2013
9080	13^46072+42	51322	Lelio R Paula	01/2013
9081	14^44778-95	51322	Lelio R Paula	01/2013
9082	11008^12697+12697^11008	51318	Norbert Schneider	01/2016
9083	t(180039)	51312	Robert Price	09/2014
9084	2^170444-443	51309	Yves Minet	05/2013
9085	(-lucasV(1,2,340915)+2)/(34091342201898187163)	51294	Mike Oakes	03/2017
9086	(2*10^51285-71)/3	51285	Robert Price	01/2017
9087	(1819288^8192+1)/65537	51277	Lelio R Paula	06/2013
9088	8907^12982-12982^8907	51276	Norbert Schneider	06/2017
9089	5^73350+28	51270	Lelio R Paula	10/2012
9090	3^107450+2	51267	Mike Oakes	11/2009
9091	2^170296+2533	51265	Henri Lifchitz	07/2004
9092	2^170293+76481	51264	Enzo Doria	05/2016
9093	11835^12584+12584^11835	51257	Norbert Schneider	11/2015
9094	(12511^12511+193)/2^5/39371	51256	Makoto Morimoto	07/2016
9096	12^47489+47489^12	51250	Serge Batalov	02/2012
9095	14637^3172+3172^14637	51250	Hans Havermann	04/2016
9097	(2^170245+7)/9	51248	Lelio R Paula	02/2012
9098	5^73308-19926	51241	Enzo Doria	03/2013
9099	8966^12963-12963^8966	51238	Norbert Schneider	06/2017
9100	3*2^170203+5	51237	Lelio R Paula	02/2014
9101	5^73300+46	51235	Lelio R Paula	10/2012
9102	2^170167+71	51226	Lelio R Paula	01/2011
9103	2^170140-15077	51218	Enzo Doria	04/2013
9104	15^43542-46	51210	Lelio R Paula	01/2013
9106	2^170111-1017	51209	Lelio R Paula	06/2008
9105	4*10^51208-87	51209	Robert Price	03/2017
9107	14^44679+83	51208	Lelio R Paula	01/2013
9108	10^51207+100147	51208	Patrick De Geest	06/2016
9109	10^51207-801	51207	Robert Price	04/2016
9110	t(170300)	51191	Robert Price	03/2015
9111	11966^12553-12553^11966	51191	Norbert Schneider	11/2016
9112	14670^3083+3083^14670	51184	Hans Havermann	04/2016
9113	99^25644-98	51177	Norbert Schneider	07/2013
9114	13211^7468+7468^13211	51169	Hans Havermann	04/2016
9115	(2^169969-1017)/35	51165	Lelio R Paula	01/2012
9116	5*10^51163-7	51164	Dmitry Domanov	11/2010
9117	(73*10^51162-1)/9	51163	Robert Price	01/2015
9118	2^169899+63	51145	Lelio R Paula	05/2009
9119	2^169898+513	51145	Lelio R Paula	05/2009
9120	3^107186-12388	51141	Enzo Doria	02/2013
9121	(12487^12487+173)/2^2/3/2917/3463/44483	51140	Makoto Morimoto	07/2016
9122	3*6^65715-7	51137	Lelio R Paula	09/2014
9123	116^24768+115	51133	Norbert Schneider	10/2013
9124	35^33113-4026	51129	Enzo Doria	03/2013
9125	(13*2^169830-1)/84477	51121	Lelio R Paula	01/2014
9126	(46*10^51111-1)/9	51112	Serge Batalov	10/2014
9127	15^43452-34	51104	Lelio R Paula	01/2013
9128	2^169750-137	51100	Lelio R Paula	01/2011
9129	2^169739+94065	51097	Lelio R Paula	10/2011
9131	15^43442-26	51092	Lelio R Paula	01/2013
9132	5^73096-17006	51092	Enzo Doria	02/2013
9130	10^51091+71601	51092	Patrick De Geest	07/2017
9133	10^51091-701	51091	Robert Price	06/2017
9134	(-lucasV(1,2,339439)-2)/(79*83)	51088	Mike Oakes	03/2017
9135	2^169706-270551	51087	Gary Barnes	08/2009
9136	(2^169696+5)/21	51083	Lelio R Paula	01/2012
9137	(1722520^8192+1)/65537	51082	Syoichiro Yamada	01/2009
9138	11^49051-8760	51082	Enzo Doria	02/2013
9139	(24737*2^169672+1)/27	51080	Lelio R Paula	05/2014
9140	2^169677+16095	51078	Lelio R Paula	05/2009
9141	2^169659-135	51073	Lelio R Paula	01/2011
9142	2^169638-113183	51067	Enzo Doria	07/2014
9143	(29*2^169622-1)/2346531185	51054	Lelio R Paula	01/2014
9144	(10^51054+17)/9	51054	Robert Price	10/2014
9145	8329^13022-13022^8329	51054	Norbert Schneider	07/2017
9146	(24737*2^169577+1)/5	51052	Lelio R Paula	05/2014
9147	11^49021-78	51051	Lelio R Paula	01/2013
9148	18^40669+61	51051	Lelio R Paula	01/2013
9149	14038^4327+4327^14038	51045	Hans Havermann	02/2016
9150	2^169555-159	51042	Lelio R Paula	01/2011
9151	91^26054-2	51041	Lelio R Paula	08/2013
9152	Phi(101775,10)/1628401	51034	Makoto Kamada	05/2015
9153	97*10^51027-3	51029	Robert Price	01/2017
9154	2^169499-2647	51025	Yves Minet	07/2014
9155	5*6^65567+7	51022	Lelio R Paula	09/2014
9156	14763^2858+2858^14763	51022	Hans Havermann	08/2015
9157	24^36966-1477	51021	Enzo Doria	03/2013
9158	(78557*2^169464+1)/160527	51014	Lelio R Paula	06/2014
9159	(34*10^51008-43)/9	51009	Ray Chandler	09/2010
9160	10^51004+128427	51005	Patrick De Geest	08/2009
9162	10^51004-113	51004	Milton L. Brown	12/2008
9161	10^51003+16951	51004	Patrick De Geest	08/2009
9163	10^51003-79601	51003	Milton L. Brown	12/2008
9164	10^51003-80831	51003	Milton L. Brown	12/2008
9165	10^51002+8877	51003	Patrick De Geest	08/2009
9167	10^51002-10541	51002	Milton L. Brown	11/2008
9166	10^51001+52051	51002	Patrick De Geest	08/2009
9168	10^51001-158687	51001	Milton L. Brown	10/2008
9169	2*10^51000+93	51001	Robert Price	07/2016
9172	(2^169416+5)/3	50999	Lelio R Paula	01/2012
9170	(49*10^50998+41)/9	50999	Robert Price	07/2015
9171	13292^6867+6867^13292	50999	Hans Havermann	02/2016
9173	(35*10^50997-71)/9	50998	Robert Price	05/2015
9174	6^65536+2*97878-1	50997	Jiahao He	05/2017
9175	29^34871-28^34871	50996	Robert Price	09/2012
9176	76^27112-75	50993	Norbert Schneider	11/2012
9177	(70^27631-1)/69	50981	Richard Fischer	08/2017
9178	(12451^12451+1345)/2^2/19/89/139/6977	50980	Makoto Morimoto	07/2016
9179	10736^12645-12645^10736	50971	Norbert Schneider	12/2016
9181	(1017*2^169315-1)/9715	50968	Lelio R Paula	03/2015
9180	7^60309-6^(60309+1)	50968	Robert Price	06/2016
9183	2^169267+99	50955	Lelio R Paula	07/2009
9182	5*2^169264+3	50955	Lelio R Paula	02/2014
9184	t(192517)	50950	Robert Price	08/2014
9185	10^50943+624451	50944	Robert Price	03/2015
9186	10^50943+54409	50944	Patrick De Geest	02/2016
9187	10^50943-100559	50943	Patrick De Geest	03/2016
9188	2^169206-3645	50937	Lelio R Paula	05/2009
9189	2^169196-112577	50934	Enzo Doria	06/2014
9190	20^39146-3483	50931	Enzo Doria	03/2013
9191	10^50929+16849	50930	Patrick De Geest	01/2012
9193	10^50929-51	50929	Robert Price	05/2011
9192	7^60264+48	50929	Lelio R Paula	10/2012
9195	2^169167+1299	50925	Lelio R Paula	05/2009
9194	10103^12717-100	50925	Enzo Doria	07/2012
9196	3^106721-130	50919	Lelio R Paula	07/2012
9198	18225^622+622^18225	50917	Anatoly F. Selevich	11/2006
9197	(10223*2^169138+1)/1113	50917	Lelio R Paula	05/2014
9199	7*2^169125+9	50913	Lelio R Paula	02/2014
9200	(47*2^169123+1)/29	50912	Lelio R Paula	03/2015
9201	20^39131+93	50911	Lelio R Paula	01/2013
9202	(21*27^35567-94921)/26	50910	Curtis Bright	05/2015
9203	(7*2^169124-1)/9549	50909	Lelio R Paula	01/2014
9204	(12433^12433+809)/2/3/11	50907	Makoto Morimoto	07/2016
9205	13693^5212+5212^13693	50897	Hans Havermann	02/2016
9206	7*5^72813+6	50895	Lelio R Paula	09/2014
9207	5*10^50890-81	50891	Robert Price	04/2017
9208	3^106656-12028	50888	Enzo Doria	02/2013
9209	(2^169028+3)/259	50881	Lelio R Paula	01/2012
9210	2^169000-1127	50875	Yves Minet	05/2013
9211	19^39780+16	50869	Lelio R Paula	01/2013
9212	(19*2^168960+1)/5	50863	Lelio R Paula	07/2012
9213	(-lucasV(1,2,337937)-2)/(3^2*11)	50863	Mike Oakes	02/2017
9215	11^48840+46	50862	Lelio R Paula	01/2013
9214	(5*10^50861-107)/3	50862	Robert Price	01/2017
9216	20^39087-4203	50854	Enzo Doria	03/2013
9217	(12421^12421+1339)/2^4/5/43/157	50848	Makoto Morimoto	07/2016
9218	2^168907-544447	50847	Paul Bourdelais	11/2012
9219	19312^429+429^19312	50839	Anatoly F. Selevich	12/2006
9220	5^72716-13226	50827	Enzo Doria	02/2013
9221	2^168823+1025	50821	Lelio R Paula	01/2009
9222	7*10^50818-89	50819	Robert Price	01/2017
9223	2^168811+15015*168811	50818	Henri Lifchitz	02/2005
9224	2^168813-2833	50818	Yves Minet	09/2014
9225	(12413^12413+3221)/2/89	50816	Makoto Morimoto	07/2016
9226	2^168795+5385	50813	Lelio R Paula	05/2009
9227	4*3^106483+5	50806	Lelio R Paula	03/2014
9228	13^45606+4	50803	Lelio R Paula	01/2013
9229	13^45606-38	50803	Lelio R Paula	01/2013
9230	2^168746+58905	50798	Lelio R Paula	05/2009
9231	(16*10^50795-43)/9	50796	Robert Price	02/2015
9232	gcd(V(615445),5F(123089)(F(123089)-1)+1)	50794	Serge Batalov	04/2015
9233	7*10^50789-47	50790	Robert Price	02/2017
9234	2^168717-729523	50789	Paul Bourdelais	11/2012
9235	(12409^12409+136)/5^2/13/5647/473279	50788	Makoto Morimoto	07/2016
9236	(21*2^168652-1)/215	50769	Lelio R Paula	01/2014
9237	2^168629+12909	50763	Lelio R Paula	01/2011
9238	9328^12787+12787^9328	50762	Norbert Schneider	01/2016
9239	2^168627+73113	50762	Enzo Doria	04/2016
9240	2^168623+47333	50761	Yves Minet	02/2010
9241	(12401^12401+154)/3^2/5/31/59/67/97/761/863/12143	50745	Makoto Morimoto	07/2016
9242	(lucasV(1,2,337126)+2)/(5*11)	50739	Mike Oakes	02/2017
9243	8544^12901-12901^8544	50723	Norbert Schneider	05/2017
9244	(17^41221+1)/18	50720	Paul Bourdelais	03/2010
9245	10^50711+7	50712	Jason Earls	12/2007
9246	10^50711-317969	50711	Patrick De Geest	04/2009
9247	(17^41213+3^41213)/20	50710	Robert Price	08/2013
9248	(12391^12391+58)/59/211/7823	50710	Makoto Morimoto	07/2016
9249	47779!4+1024	50708	Robert Price	08/2017
9250	2^168431-159	50703	Lelio R Paula	01/2011

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PRP Records

Probable Primes Top 10000

(181746 PRPs in the top)